An R-C circuit is driven by an alternating voltage of amplitude 110 and frequency . Define to be the amplitude of the voltage across the capacitor. The resistance of the resistor is 1000 , and the capacitance of the capacitor is 1.00 . I need help on what to do I'm lost thanks.
Vc = Q/C
Vr = i R
V = Vc+Vr if in series
here i = I cos wt
Q = integral idt = (I/w) sin wt
Vc = (I/wC) sin wt
Vr = IR cos wt
so
V = I [ (1/wC) sin wt + R cos wt ]
but
given V = 110 sin(wt+P) where P is some phase angle
Trig identity
V = 110 [ sin wt cos P + cos wt sin P]
so
110 cos P = I/wC and 110 sin P = IR
110^2 cos^2 P = (I/wC)^2
110^2 sin^2 P = (IR)^2
add
110^2 (1) = I^2 [(1/wC)^2 + R^2 ]
so
If you know w, C and R
you can get I right there
Now you want Vc ?
we know Vc = (I/wC) sin wt
we know I, w and C so we know the amplitude of Vc
To find the amplitude of the voltage across the capacitor (Vc), we can use the concept of complex impedance. In an R-C circuit driven by an alternating voltage, the complex impedance is given by:
Z = R + 1/(jωC)
Where:
Z is the complex impedance
R is the resistance
j is the imaginary unit (sqrt(-1))
ω is the angular frequency (2π times the frequency)
C is the capacitance
Since we are given the resistance (R) as 1000 ohms and the capacitance (C) as 1.00F, we can substitute these values into the equation:
Z = 1000 + 1/(jω * 1.00F)
The angular frequency (ω) is not given in your question, so we do not have enough information to calculate the exact value of Z. However, we can proceed by assuming a value of ω and solving for Z, and then find Vc using Ohm's Law.
Once we have Z, the voltage across the capacitor (Vc) can be calculated as:
Vc = V / |Z|
Where:
V is the amplitude of the driven voltage (given as 110)
Remember, this approach assumes a certain value for ω. If you have the frequency, you can calculate ω as 2π times the frequency to use in the equations above.